WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Optimal System for non-linear Burger equation $$u_{t} = u_{xx} + uu_{x·}$$
Authors: ,
Abstract: The paper discusses the optimal system for a nonlinear Burger equation whose coefficients are dependent
on first order spatial derivatives. The main purpose for the project is to determine the optimal system for the operators
accepted by the equation. We construct the principal Lie algebra, calculate transformations for the generators
which provide one-parameter group of transformations for the operator using Lie equations. We construct optimal
systems for the equation where the method requires a simplification of a vector to a general form for each of the
transformations of the generators. These are finally used to determine invariant solutions for some operators.